Question

Find the equation for the family of lines tangent to the circle with center at the origin and radius 3.

Answer 1

I know, use the equation y=mx+c. But how?

Answer 2

First draw the circle

Answer 3

Yes, but, well

I also believe we should apply equation of a circle as well to this

Answer 4

tangent is perpendicular to the radius of the circle. and slope of perpendicular line are m1=-1/m2. right??

Answer 5

yes

Answer 6

let us simplify the question first.
we just find the equation of tangent line and then find the family. OK

Answer 7

Let me get back to you regarding this question. I think they want more than just the equation of a tangent line at one point on the circle. I think they want an equation of a tangent for any point on the circle

Answer 8

yes yes. exactly. family of line implies this idea as you said.
but if we find equation for one tangent the we can find equation for any tangent. family too.

Answer 9

did you get my idea?

Answer 10

if you found an equation for one tangent, you would not be able to find it for another tangent. That would only work if (3,0), (-3,0)(0,3)(0,-3) were the points

Answer 11

You would already have to know the points in advance for any other point on the circle in order to find the equations of tangent lines

Answer 12

look Hero.
y=-x+c is the family of line which has same slope.
do you know this idea?
If so then why not for above question?

Answer 13

What concepts are you studying in class regarding this? Are you working from a textbook? If so, tell me the name of the section you're working on.

Answer 14

Calculus by howard anton. 7th edition

Answer 15

Oh, I see. This is calculus. I thought you were doing high school geometry

Answer 16

it is university level.

Answer 17

our circle is\[x^2+y^2=9\]the formula for a tangent line at a point 'a' is\[y-y(a)=y'(a)(x-a)\]I think we should differentiate implicitely to get y'

Answer 18

no. differentiation is not include up to this section. so we can't differentiate it.

Answer 19

eh? um....
then how is it calculus?

Answer 20

look look..
it is 1st chapter named functions
and differentiation is starting from chap#3

Answer 21

no one can help me on this problem :(

Answer 22

ok um...
let's see if we can be creative based on what we know from functions and trig
the following are tangent lines to the circle\[x=\pm3\]\[y=\pm3\]that covers four sidesnow we need to develop some formulas for the areas in between the top, bottom, left, and right

Answer 23

hm...here is a tangent line at some mystery point, I wonder if we can divine a formula for the slope of it

Answer 24

heheheheh... divine..

Answer 25

maybe we can use some trig here...